Related papers: The Induced Bipartite Ramsey Theorem: An Expositio…
We prove that finite partial orders with a linear extension form a Ramsey class. Our proof is based on the fact that class of acyclic graphs has the Ramsey property and uses the partite construction.
We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.
We give a proof of a Martingale Representation Theorem using the methods of nonstandard analysis.
We use the model theoretic notion of coheir to give short proofs of old and new theorems in Ramsey Theory. As an illustration we start from Ramsey's theorem itself. Then we prove Hindman's theorem and the Hales-Jewett theorem. Finally, we…
Bipartite experiments are a recent object of study in causal inference, whereby treatment is applied to one set of units and outcomes of interest are measured on a different set of units. These experiments are particularly useful in…
We prove an infinite Ramsey theorem for noncommutative graphs realized as unital self-adjoint subspaces of linear operators acting on an infinite dimensional Hilbert space. Specifically, we prove that if V is such a subspace, then provided…
We prove some results on the border of Ramsey theory (finite partition calculus) and model theory. Also a beginning of classification theory of finite models in undertaken.
We present a new, category theoretic point of view on finite Ramsey theory. Our aims are as follows: -- to define the category theoretic notions needed for the development of finite Ramsey Theory, -- to state, in terms of these notions, the…
In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
Ramsey's theorem states that each coloring has an infinite homogeneous set, but these sets can be arbitrarily spread out. Paul Erdos and Fred Galvin proved that for each coloring f, there is an infinite set that is "packed together" which…
This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.
We expose here a short proof of Cramer's theorem in R based on convex duality.
Inspired by the inductive proof of LYM-inequality given by P. Frankl, we provide an inductive proof of the Bollob\'{a}s two family theorem.
We prove a noncommutative version of Bishop's peak interpolation-set theorem.
The classical Ramsey theorem was generalized in two major ways: to the dual Ramsey theorem, by Graham and Rothschild, and to Ramsey theorems for trees, initially by Deuber and Leeb. Bringing these two lines of thought together, we prove the…
In this paper we give a proof of an index theorem by Bismut. As a consequence we obtain another proof of the Grothendieck-Riemann-Roch theorem in differential cohomology.
We give a probalistic proof of the famous Meinardus' asymptotic formula for the number of weighted partitions with weakened one of the three Meinardus' conditions, and extend the resulting version of the theorem to other two classis types…
We give an abstract approach to finite Ramsey theory and prove a general Ramsey-type theorem. We deduce from it a self-dual Ramsey theorem, which is a new result naturally generalizing both the classical Ramsey theorem and the dual Ramsey…
Let $G$ be a locally compact second countable groupoid with a Haar system. In this article, we introduce the induced representation of $G$ from a continuous unitary representation of a closed wide subgroupoid $H$ with a Haarsystem provided…